Finding Exact Value of Trig Expression

[whatisphysics]

Homework Statement

Find the exact value of each expression:
a) sec^-1($$\sqrt{}2$$)
b) sin^-1(1)

Homework Equations

sec$$\theta$$=$$\stackrel{}{}1/cos\theta$$

The Attempt at a Solution

I've never learned this, but I am really curious in how it is solved.
Is there a formula for this? Thanks!

 

[iamalexalright]

These are inverse functions so:

a. For what value of x does sec(x) = sqrt(2)

b. For what value of x does sin(x) = 1?

 

[Mark44]

Homework Statement

Find the exact value of each expression:
a) sec^-1($$\sqrt{}2$$)
b) sin^-1(1)

Homework Equations

sec$$\theta$$=$$\stackrel{}{}1/cos\theta$$

The Attempt at a Solution

I've never learned this, but I am really curious in how it is solved.
Is there a formula for this? Thanks!

Do you understand inverse functions?

IOW, x = f^-1(y) <==> y = f(x)

For example, suppose you were asked to find cos^-1(1/2).

Let y = cos^-1(1/2).
That is equivalent to 1/2 = cos(y). What angle in the interval [0, $\pi$] has a cosine of 1/2?

 

[whatisphysics]

Do you understand inverse functions?

IOW, x = f^-1(y) <==> y = f(x)

For example, suppose you were asked to find cos^-1(1/2).

Let y = cos^-1(1/2).
That is equivalent to 1/2 = cos(y). What angle in the interval [0, $\pi$] has a cosine of 1/2?

Should I memorize the circle with all the angles?
And this may sound silly...but on (x,y), which is cos and sin? Is it like (cos, sin) on the circle, or the opposite?

 

[Mark44]

On the unit circle, x = cos(t) and y = sin(t).

 

[hunt_mat]

A simple way to look at the problem is let $$a=\sec^{-1}\sqrt{2}$$ then $$\sec a=\sqrt{2}$$. From here it is easy to compute the value a by turning sec into cos and using information about known values of cos.

 

[whatisphysics]

Thank you all for the input! I think I will learn to memorize the circle with all the angles...I'm sure that will help.